Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin’s more general framework and I characterise what Maudlin’s topological concepts boil down to when applied to discrete linear (...) structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin’s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin’s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On the one hand, my theorems support (a): the theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b): standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin’s framework. This fact poses a challenge for the proponents of Maudlin’s theory to prove it fruitful. (shrink)

The aim of this paper is to present a new logic-based understanding of the connection between classical kinematics and relativistic kinematics. We show that the axioms of special relativity can be interpreted in the language of classical kinematics. This means that there is a logical translation function from the language of special relativity to the language of classical kinematics which translates the axioms of special relativity into consequences of classical kinematics. We will also show that if we distinguish a class (...) of observers in special relativity and exclude the non-slower-than light observers from classical kinematics by an extra axiom, then the two theories become definitionally equivalent. Furthermore, we show that classical kinematics is definitionally equivalent to classical kinematics with only slower-than-light inertial observers, and hence by transitivity of definitional equivalence that special relativity theory extended with “Ether” is definitionally equivalent to classical kinematics. So within an axiomatic framework of mathematical logic, wee xplicitly show that the transition from classical kinematics to relativistic kinematics is the knowledge acquisition that there is no “Ether”, accompanied by a redefinition of the concepts of time and space. (shrink)